# Geometry B

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A solid has 10 faces: 4 triangles;1 Square; 4 hexagons; and 1 octagon, how many vertices does the solid have?

• Geometry B -

Euler showed that F+V-E=2, so now we know that

E-V = 10
Since each edge belongs to two polygons, there are (4*3+1*4+4*6+1*8)/2 = 24 edges

So, there are 14 vertices

seems reasonable, since all vertices belong to 3 or mlore polygons

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